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4.2 Rectilinear Particle Motion 101

Consequently, it is not necessary to know the physical size, shape or density of a
particle if its aerodynamic diameter is determined.
From the above equation, one can get the formula for aerodynamic diameter,

1 =2
q p

d ¼ d e ð4:26Þ
a
q S f
0
Example 4.3: Aerodynamic diameter
Estimate the aerodynamic diameter of a spherical steel particle with a geometric
3
equivalent diameter d e =10 μm and ρ p = 8,000 kg/m .
Solution
Since the particle is spherical, its shape factor, S f =1

q 8000
1=2 1=2
p 6 5
d a ¼ d e ¼ 10 10 ¼ 2:83 10 m ¼ 28:3lm
q S f 1000 1
0
For a particle with this great density, its aerodynamic particle diameter is much
greater than its geometric equivalent diameter.

4.2.4 Curvilinear Motion of Aerosol Particles

Curvilinear motion is a motion when a particle follows a curved path. A classic
example of curvilinear motion is the projectile of a particle with a horizontal initial
velocity in the still air. It is more complicated for a particle-air mixture that flows
around an obstacle. Very small particles with negligible inertia tend to follow the
gas while large and heavy particles tend to continue in a straight line due to the
great inertia.
The inertia of a particle in curvilinear motion is characterized by the Stokes
number (Stk), like the Reynolds number in fluid mechanics for the characterization
of a fluid flow. The Stokes number is defined as the ratio of the stopping distance of
a particle to a characteristic dimension of the obstacle.

2
su 0 q d C c u 0
p p
Stk ¼ ¼ ð4:27Þ
d c 18ld c
where the characteristic dimension d c in the above equation can be defined dif-
ferently according to applications. And the definition of Stokes number may be
application specific. u 0 is the undisturbed air speed. In standard air, a particle with
Stk ≫ 1.0 will continue in a straight line as the fluid turns around the obstacle. But
for a particle with Stk ≪ 1, it will follow the fluid streamlines closely.